Balancing Equations, Reacting Masses, Limiting Reagents, and Yield

A balanced chemical equation is the foundation of every quantitative calculation in chemistry because it expresses the ratio in which substances react and form. The law of conservation of mass requires that atoms are neither created nor destroyed in a reaction, so the number of atoms of each element must be equal on both sides of the equation. We balance equations by placing coefficients in front of formulas, never by changing subscripts, since changing a subscript would change the identity of the substance. Consider the combustion of methane. The unbalanced equation $CH_4 + O_2 \rightarrow CO_2 + H_2O$ is balanced by adjusting coefficients to $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$, which gives one carbon, four hydrogens, and four oxygens on each side.

The coefficients in a balanced equati